Roots and coefficients of a quadratic equation

Question 1

sum of the roots

Answer 1

-b/a

Question 2

product of the roots

Answer 2

c/a

Question 3

-b/a

Answer 3

sum of the roots

Question 4

c/a

Answer 4

product of the roots

Question 5

x^2+_____x+________=0

Answer 5

x^2-{sum of roots}x+{product of roots}=0

Question 6

Find the equation of the quadratic equation where the roots are α^2 and β^2 in terms of α and β

Answer 6

sum = α^2 + β^2=(α+β)^2 - 2αβ
product = α^2β^2 = (αβ)^2

Question 7

Find the equation of the quadratic equation where the roots are α^3 and β^3 in terms of α and β

Answer 7

sum = α^3 + β^3 =(α+β)^3 - 2αβ(α+β)
product = α^3β^3 = (αβ)^3

Question 8

Find the equation of the quadratic equation where the roots are α+1 and β+1 in terms of α and β

Answer 8

sum = α+1 + β+1 = α+β+2
product = (α+1)(β+1) = αβ + (α+β) + 1

Question 9

Find the equation of the quadratic equation where the roots are 1/α and 1/β in terms of α and β

Answer 9

sum = 1/α + 1/β = (α+β)/αβ
product = 1/α * 1/β = 1/(αβ)